ABSTRACT
The ‘geometry’ of flocks of quadratic cones has now reached into many diverse areas of incidence geometry. For example, it is know that if there is a translation plane of order q2 with spread in PG(3, q) that admits a Baer group of order q (fixes a Baer subplane pointwise) there is a corresponding flock of a quadratic cone. In Johnson [726], it was shown that the q − 1 orbits of length q of the Baer group on the components of the spread define reguli that share the pointwise fixed subspace, which, in turn, defines a partial flock of deficiency one of a quadratic cone. Payne and Thas [1094] then show that any deficiency-one partial flock may always be extended to a flock of a quadratic cone. This means that the net of degree q + 1 defined by the components of the Baer subplane is a regulus net and by derivation of this net, there is an associated translation plane with spread in PG(3, q) where the Baer group now becomes an affine elation group. We call such elation groups ‘regulus-inducing’.
